Scaling between structural relaxation and caged dynamics in Ca_(0.4)K₀.6(NO₃)_(1.4) and glycerol: free volume, time scales and implications for the pressure-energy correlations

The scaling of the slow structural relaxation with the fast caged dynamics is evidenced in the molten salt Ca_{0.4}K_{0.6}(NO_{3}$)_{1.4} (CKN) over about thirteen decades of the structural relaxation time. Glycerol caling was analyzed in detail. In glycerol, the short-time mean-square displacement <u^2>, a measure of the caged dynamics, is contributed by free-volume. It is seen that, in order to evidence the scaling, the observation time of the fast dynamics must be shorter than the time scales of the relaxation processes. Systems with both negligible (like CKN, glycerol and network glassformers) and high (like van der Waals liquids and polymers) pressure-energy correlations exhibit the scaling between the slow relaxation and the fast caged dynamics. According to the available experiments, an isomorph-invariant expression of the master curve of the scaled data is not distinguishable from a simpler not-invariant expression. Instead, the latter grees better with the simulations on a wide class of model polymers.